GaussianEliminationWithPartialPivoting

Project 1: Gaussian Elimination with Partial Pivoting

This project was assigned for the Numerical Methods for Electrical Engineering (EE 242) course in the Spring 2021 semester.

Run on Terminal

g++ main.cpp -o test
test A.txt b.txt

Project Goals

In this project, you will be implementing the Gaussian elimination algorithm with partial pivoting together with backward substitution to solve Ax = b, where A is an n by n square matrix.

Your program should read A and b from two input text files and output the solution x as a text file.

Programming Details

Your program should,

• read A matrix from A.txt file and b vector from b.txt file. Each line in a file represents a row,
• use dynamically allocated memory to store the matrix and the vector,
• print out an error message and quit if it detects that A is singular, (Don’t forget to consider the machine precision while detecting singularity.)
• print out the elements of the solution x (in the correct order) and write them in a text file.

The Case of High Condition Numbers

• In order not to add a great amount of burden onto this project, you do not have to find the condition numbers for every given matrix. However, in the case of 2x2 matrices, your program is required to output the condition numbers using 1 - norm and infinity-norm. (You can print these on the screen; they are not required in a text file.)